Evaluate (10 – 41) ÷ (5 + 1).

(9¹²)⁷

Use the rules of exponents to simplify the expression. To raise a power to another power, multiply the exponents.

9¹² ˣ ⁷

Multiply 12 by 7.

9⁸⁴

Answer: 9^84 is the answer!

Step-by-step explanation:

The piecewise function on the graph is,

f(x) = {  1 -3x ; if x ≤ 2

        { 4-x    ; if x > 2

The graph of a piecewise function is given. The left function is defined on the interval x ≤ 2 and the right function is defined on the interval x > 2.

To find the functions we need two points on each function since both functions are straight lines.

First we will find the left function defined on x ≤ 2.

So the two points are (x₁, y₁) = (0,1) and (x₂, y₂) = (2, -5).

Now slope of the left function, m₁ = (y₂ - y₁)/(x₂ - x₁)

                                                        = -5 - 1/2 - 0

                                                        = -6/2

                                                        = -3

So the equation of the left function is,

y - y₁ = m(x-x₁)

⇒ y - 1 = -3(x-0)

⇒ y = 1 -3x

Thus the left function is f(x) = 1 -3x

Consider the right function.

The two points on the graph of the right function are (x₁, y₁) = (4,0) and (x₂, y₂) = (6, -2).

So slope of the second function, m₂ = (y₂ - y₁)/(x₂ - x₁)

                                                            = -2 - 0/6-4

                                                            = -2/2

                                                            = -1

Now equation for the right function is,

y - y₁ = m(x-x₁)

⇒ y - 0 = -1(x-4)

⇒ y = 4 -x

So the right function is f(x) = 4-x

Hence the piecewise function is,

f(x) = {  1 -3x ; if x ≤ 2

        { 4-x    ; if x > 2

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Answer:

B

Step-by-step explanation:

4x + 2 = 22 ( subtract 2 from both sides )

4x = 20 ( divide both sides by 4 )

x = 5

The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet

From the question, the given parameters are

Area = 903 square feet

Shape = rectangle

From the question, we understand that:

One side of the area would be enclosed by the external wall of the store

If the dimensions of the area are Length (L) and Width (W), then we have

Area = LW

Perimeter = 2L + W

Rewrite as

A = LW

P = 2L + W

Substitute 903 for A in A = LW

LW = 903

Make W the subject

W = 903/L

Substitute W = 903/L in P = 2L + W

P = 2L + 903/L

Differentiate the equation

So, we have

P' = 2 - 903/L²

Set to 0

2 - 903/L² = 0

So, we have

903/L² = 2

This gives

L² = 903/2

Divide

L² = 451.5

Take the square roots

L = 21.25

Substitute L = 21.25 in W = 903/L

W = 903/21.25

Evaluate

W = 42.50

Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet

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Slavery and oppression of other people impact others as it brings about discrimination and fear.

In the olden days, slavery was so lucrative that the Mississippi River valley produced more millionaires per capita than any other region of the country. With cash crops like tobacco, cotton, and sugar cane, the southern states of America developed into the country's economic engine.

In Africa, the slave trade had a terrible impact. A culture of lawlessness and violence was encouraged by the financial incentives provided to warlords and tribes to participate in the slave trade. Economic and agricultural development in a large portion of western Africa was virtually impossible due to depopulation and a persistent fear of enslavement.

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Answer:

Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.

Explanation:

P(25, 10) lies on the curve:

Q is the point (x, √x+5).

For any value of x, the slope of the secant line PQ is determined using the formula:

(a)When x=25.1

(b)When x=25.01

(c)When x=24.9

(d)When x=24.99

Based on the results above, the slope of the tangent line to the curve at P(25,10) is 0.1.

The value of x in the equation given as 1/6(x - 3) = 1/3(x + 2) is 7

The equation is given as

1/6(x - 3) = 1/3(x + 2)

From the question, we can see that the equation is a linear equation with one variable

As a general rule: linear equations are equations that have constant average rates of change.

We start by multiplying both sides of the equation by 6

So, we have the following equation

6 * 1/6(x - 3) = 1/3(x + 2) * 6

Next, we evaluate the products

So, we have the following equation

x - 3 = 2x + 4

Next, we collect the like terms

So, we have the following equation

2x - x = 3 + 4

Evaluate the like terms in the above equation

x = 7

This means that the solution of the equation is 7

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1 rad x 180/pi =57.296 deg

so the answer is 744.845

Answer:

x = 61/2 = 30.5 = 60 1/2

Step-by-step explanation:

We have:

We have to find the Least Common Multiple to solve this question:

The square roots would not be between 9 and 10 is [tex]\sqrt{80}[/tex].

[tex]\sqrt[]{80}=8.944\\ \sqrt[]{90}=9.486\\ \sqrt[]{95}=9.746\\ \sqrt[]{88}=9.380[/tex]

What are square roots?

The opposite of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number may be found by looking for a number that, when squared, yields the original value. It follows that a, a = b if "a" is the square root of "b." Every integer has two square roots, one of a positive value and one of a negative value because the square of any number is always a positive number. For instance, the square roots of 4 are both 2 and -2. However, the square root of a number is typically only expressed as the positive value.

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way. It is symbolized by the character "." The number behind the square root sign is referred to as the radicand, whereas the square root symbol itself is known as a radical.

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EXPLANATION

Given the expression 12(3y+x).

Let's solve it:

Applying the distributive property:

12*3y + 12*x

Multiplying like terms:

36y + 12x

The answer is 36y + 12x

STEP - BY - STEP EXPLANATION

What to do?

Apply the distributive property on the given expression.

Given:

Step 1

Explain what the distributive property mean.

Distributing -1 implies multiplying -1 by each term.

Step 2

Apply the distributive property.

ANSWER

-6v + 4u +1

If the average number of babies born at a private hospital's maternity wing is 6 per hour. The probability that three babies are born during a particular 1-hour period in this maternity wing is 0.09.

Mean = 6 per hours

Number of babies = 3 babies

Hence,

Now let determine the probability

Let x represent the probability

Pr(X=3) = e^-6 × 6^3 ÷ 3!

Pr(X=3) =0 .535410 ÷ 6

Pr(X=3) = 0.089

Pr(X=3) =0.09 (Approximately)

Therefore we can conclude that 0.09 is the probability.

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a) triangle with measurement 1/2 of the original measurement.

b)  rhombus with measurement  2 times the original measurement.

c) parallelogram with measurement 1/4 of the  original measurement.

The polygon is 2- dimensional figure and is any closed curve made of continuous edges also called the sides without intersecting each other,  the corner of a  polygon is called the vertices, the are of basically two types regular and irregular, whereas The scale factor a polygon the ratio of one side of a polygon to the comparing side of the other is called the scale factor. The proportion of all parts of a polygon, including diagonals,  perimeter, and heights is the same as the proportion of the sides.

a) the given scale factor is 1/2  and, we need to construct a scale copy of the triangle having sides measurements 1/2 of the original measurements.

b) the new polygon must have the measurements 2 times the original measurements of the polygon .

c) the new polygon must have dimensions 1/4 of the dimensions of the original measurements.

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The given expression is

To add 2 fractions we have to give them the same denominators

In the up part (numerator) we have 2 different denominators a and b

Then the common denominator of the 2 fractions must be the product of them

Then the fraction will be

Now, we will multiply the denominator of up by the denominator of the first fraction (ab x b)

Multiply b by b to simplify, then

The numerator is 2b + 7a

The denominator is ab^2

Given the equation:

Let's solve for x.

To find the solution, take the following steps:

Step 1:

Apply the product property of logarithm to the left side of the equation:

Step 2:

Eliminate the log on both sides

Step 3:

Subtract x from both sides

Step 4:

Divide both sides by 2

Therefore, the solution to the given equation is:

ANSWER:

The equation is PV = nRT.

The calculations for the ideal gas law are comparison of the Pressure and Volume of gas based upon amount and temperature.

The basic formula is PV = nRT where

P = Pressure in atmospheres (atm)

V = Volume in Liters (L)

n = number of moles (mol)

R = the Ideal Gas Law Constant

T = Temperature in Kelvin (K)

The value of n is the amount of the gas measured as moles.

One may need to convert a mass to moles by dividing the given mass of the gas by the molar mass of the gas to get moles.

Hence, The equation is PV = nRT.

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Step 1

State the formula for the area of a trapezoid

Step 2

Find the height

Hence, the height = 5m

Answer:

7x+9=8

Step-by-step explanation:

4-x+7x-1-8-5x+6x+13

=7x+8

:]

Answer:

70 points

Step-by-step explanation:

u = US points

c = Canadian points

n = Norwegian points

u = c + 2

n = c - 4

208 = u + c + n

208 = ( c + 2 ) + c + ( c - 4 ) = 3c - 2

Isolate c:

208 = 3c - 2

210 = 3c

c = 70

Answer:

17.03 cm

Step-by-step explanation:

Use the Pythagorean theorem, which states a^2+b^2=c^2. 13^2+11^2=290, sqrt290 cannot be simplified down into a whole number, therefore the next closes rounded to the nearest tenth is 17.03.

Answer:

644

Step-by-step explanation:

-4x23=-92

-92x-7=644

hope this helped :)

Answer:

644

Step-by-step explanation:

if you multiply -4 by 23 it equals -92 and then if you multiply -92 by -7 it comes out to a positive 644 because if multiplying a negative by a negative it becomes a positive.

thank you for your question and let me know if it is right or wrong

blessings!

Recall that in a geometric sequence, whenever we take one value of the sequence and divide it by the next number of the sequence, we would get a constant number unique to that sequence. If we take the first and second numbers and calculate the ratio, we get

if we do that with the second and third numbers, we get

this two numbers should be equal. So we get

if we multiply both sides by 3, we get

so option A is the correct option.

In order to add these numbers, first let's write all of them with the same number of decimal places:

17.34 = 17.340

8.03 = 8.030

0.009 = 0.009.

Then, let's add all algarisms that are in the same position in each number:

0 + 0 + 9 = 9

4 + 3 + 0 = 7

3 + 0 + 0 = 3

7 + 8 + 0 = 15 (5 plus 1 to next algarism)

1 + 0 + 0 (+ 1) = 2

So the final result is 25.379.

We can see two graphs and we need to determine the reason why graph A IS a function, and graph B is NOT a function.

To achieve that, we can proceed as follows:

1. A function is a relation in which for each element of the domain we have only (exactly) one element of the range.

2. The domain of a function is the values for x for which the function is defined, and the range is those values for y that result when the function takes values for x and after following the rule of the function (the values for which the function is defined).

3. To determine if a graph is a function, we can use the vertical line test. Given the above definitions, this test tells us that if a vertical line passes through a graph at more than a point, then the relation is NOT a function.

4. Now we can use the Vertical Line Test on each graph as follows:

As we can see from the graph, the vertical line passes through only one point (one value for y associated to x). We can see that the open circle indicates that the function is not defined for the value while the solid circle indicates that the function is defined for that value.

For instance, for x = -1 the value of the function is y = 0 (and not y = -1 - see the open circle). We have a similar case for x = 1 (y = 1) (not y = 0).

Therefore, graph A IS a function.

In this case, we can say that the vertical line passes through more than one point in most of the values. However, we can say that there are some values where the line passes through one point - from x = -3 to x = -2 (included) -, and for values greater than 2 (x>2).

However, since the vertical line test indicates that the line passes through more than a point (there are more than a value, y, for each x) then Graph B is NOT a function.

Therefore, in summary, we can say that using the method of the vertical line test, Graph A IS a function, while Graph B is NOT a function.

Answer:

19π/12

Explanation:

We know that

180 degrees = π radians

and we are asked

285 degrees = ? radians?

This can be treated as a ratio problem by saying that

where x is the angle in radians.

Cross multpication gives

dividing both sides by 180 gives

where we have used the fact that 285/12 = 19/12.

We can represent this situation with a triangle, as shown below:

We need to calculate the angle that forms between the line of sight of the Life Guard and the swimmer. For that, we will have to use the tangent relation.